We examine the problem of reconstructing the order of DNA fragments that are produced by restriction digests as they appear in the original DNA sequence. Established procedures that work for DNA segments in the 5-10 Kb range do not work for human chromosomal size DNA (approx. 100,000 Kb). It is assumed that multiple copies of an original DNA segment have been digested with one or more enzyme digests in such a way that overlapping fragments of the original DNA are created. The size of the fragments should be appropriate to cloning in some bacterial system or in yeast (where larger fragments, 200Kb, have been cloned), and a "library" consisting of clones of these fragments is assumed. The overlapping fragments may be obtained by partial digestion of the DNA by a single enzyme or total digestion by two or more enzymes used individually. The critical step is to identify as many pairs of overlapping fragments as possible. If the library covers the chromosomal DNA and all intersecting pairs can be identified, a minimal sequence of overlapping fragments reaching from one end of the DNA to the other may be obtained. Determination that two fragments overlap can be made by further digestion of each of the fragments into smaller pieces and observing that two pieces, one from each fragment, are identical. Questions that arise are what numbers and sizes of fragments are produced by different digestion protocols, what fraction of the DNA is covered by the clonable fragments, and what is effectiveness of different procedures for determining that pieces of fragments are identical.